Program

Abstract: The heart fan is a new convex-geometric invariant of an abelian category which captures interesting aspects of the related homological algebra. I will review the construction and some of its key properties, illustrating them through examples. In particular I will explain how the heart fan can be viewed as auniversal phase diagram' for Bridgeland stability conditions with the given heart. This is joint work with Nathan Broomhead, David Pauksztello and David Ploog (arXiv:2310.02844v2).

Abstract: In this talk, we propose notions of generically tame and generically wild τ-tilting types of finite-dimensional algebras. We show a trichotomy into finite, generically tame and generically wild τ-tilting type for algebras associated to symmetrisable generalised Cartan matrices. These algebras were introduced by Geiß-Leclerc-Schröer and are degenerations of hereditary algebras; but  they are often of wild representation type even if the corresponding  Cartan matrix is of finite or affine type.

Abstract: I will present a new development of a project in collaboration with Francesco Esposito, Ghislain Fourier and Fang Xin whose aim is to define and study a specialization map for quiver Grassmannians of Dynkin type. The project started in 2018. A first draft of the result obtained was put on the arXiv in 2022. This year we found a much better approach that I will explain in the seminar. We prove that the specialization map is surjective in type A. This generalizes a beautiful theorem of Lanini and Strickland concerning the cohomology of degenerate flag varieties. arXiv: 2206.10281

Abstract: The constructible derived category of P^n is equivalent to the bounded derived category of the principal block of parabolic category O for sl_n, and also to the bounded derived category of a certain special biserial algebra. In both of these languages, the Serre functor can be explicitly described: from the perspective of category O, results of Mazorchuk--Stroppel describe it as a concatenation of shuffling functors, and from the perspective of finite-dimensional algebras, results of Happel describe it as the Nakayama functor. In this talk, I will explain a description of the Serre functor from the perspective of perverse sheaves. This is joint work in progress with Alessio Cipriani.